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Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

Published online by Cambridge University Press:  01 April 2000

M. C. A. M. BINK ,
L. L. G. JANSS  and
R. L. QUAAS
M. C. A. M. BINK
Affiliation:
Animal Breeding and Genetics Group, Wageningen Institute of Animal Sciences, Wageningen Agricultural University, Wageningen, PO Box 338, 6700 AH, The Netherlands Current address: Centre for Biometry Wageningen (CBW), DLO – Centre for Plant Breeding and Reproduction Research (CPRO-DLO), PO Box 16, 6700 AA, Wageningen, The Netherlands. Tel: +31 317 477306. Fax: +31 (0)317 418094. e-mail: [email protected]
L. L. G. JANSS
Affiliation:
Institute for Animal Science and Health (ID-DLO), 8200 AB Lelystad, The Netherlands
R. L. QUAAS
Affiliation:
Department of Animal Science, Cornell University, Ithaca, NY 14853-4801, USA

Abstract

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A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the ‘Fernando and Grossman’ multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the ‘Fernando and Grossman’ model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.

Type
Research Article
Information
Genetics Research , Volume 75 , Issue 2 , April 2000 , pp. 231 - 241
Copyright
© 2000 Cambridge University Press